Solving a quadratic equation via factorisation (or otherwise) with the $x^2$-term having a coefficient of 1.

Solving a pair of simultaneous equations of the form $a_1x+y=c_1$ and $a_2x^2+b_2xy=c_2$ by forming a quadratic equation.

Solving a pair of linear simultaneous equations, giving answers as integers or fractions.

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant.

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Solving first order differentials by separation of variables.

Practice question solving linear homogeneous second order differentials using the auxiliary equation method.

Solving an equation of the form $ax \equiv b\;\textrm{mod}\;n$ where $a$ and $n$ are coprime.

Solving $\cos(nx)=a$ for $x\in (0,\pi)$, where $n$ is an integer and $a\in(0,1)$.

Solving a pair of simultaneous equations of the form $a_1x+b_1y=c_1$ and $a_2 x^2+b_2y^2=c_2$ by forming a quadratic equation.

Solving a pair of simultaneous equations of the form $a_1xy=c_1$ and $a_2x+b_2y=c_2$ by forming a quadratic equation.

In parts (a) and (b) rearrange linear inequalities to make $x$ the subject.

In the parts (c) and (d) correctly give the direction of the inequality sign after rearranging an inequality.

Solving a pair of linear simultaneous equations with integer solutions.

Solving a pair of linear simultaneous equations, giving answers as integers or fractions.

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Solving a quadratic equation via factorisation, with the $x^2$-term having a coefficient of 1.

Solving a cubic equation of the form $ax^3+bx^2+cx+d=0$.

Solving binary optimisation problems using Computational Packages

Solving continuous optimisation problems using Computational Packages

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

Recovering original function given some information such as derivative and value at some point.

A quadratic equation (equivalent to $(x+a)^2-b$) is given and sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.

Finding X-Y intercepts for quadratic and cubic equations.

A few quadratic equations are given, to be solved by completing the square. The number of solutions is randomised.

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Solving a differential equation of the form $\frac{dy}{dx}=\frac{ax^n}{y}$ using separation of variables.

Solving a differential equation of the form $\frac{dy}{dx}=axy^2$ using separation of variables.

Solving a differential equation of the form $\frac{dy}{dx}=axy$ using separation of variables.

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